Question

Question #7a536

Answer 1

if the circumference is `9pi`, then `A ~~3.53` , but if the area of the whole circle is `9pi`, then `A =pi/2`

Explanation:

So I'm asuming you have a circle with a circumference of `9pi` in wich you want the area of a sector?

If the angle that forms the sector is given in radians, then we can use the formula: `A=1/2r^2theta`
In this case, `theta=1/9pi`

We don't know the radius, therefore we must find it first.
The circumference of a circle is given by: `O = 2rpi`
Therefore:
`9pi=2rpi iff 9=2r iff r = 4.5`

Now we can calculate the area of the sector: `A=1/2*4.5^2*1/9pi ~~ 3.53`

... Or maybe, you meant the are of the whole circle is `9pi` in many ways this would make more sense.

The solution is found in a similar way, only we will have to define two areas. The area for the whole circle and the area of the sector:
Aw is the area of the Whole circle.
`A_"w" = r^2pi = 9pi`

Isolate "r".

`r^2pi = 9pi iff r^2=9 iff r = sqrt9=3`

Now calculate the area of the sector in the same way we did before:

`A_"s"=1/2*3^2*1/9pi = pi/2`

This answer looks much better, which is why I think this is more correct.

Sorry for the inconvienience